In the fundamental physics of the world, there is neither space nor time
nautil.us
nautil.us
I recommend the book, it was an enjoyable read. The author is able to explain clearly concepts that I had struggled to understand before.
Throughout the book there are a many references to philosophical ideas and to the history of science, in some cases quite emotional. This being the last chapter, is quite heavy on them. However, I found them quite useful and interesting as a tool to break from preconceived notions of time.
If fundamentally there is no time, then fundamentally there is only eternity.
A much simpler but perhaps more tedious way out of this apparent rational loophole for religions would be accept it. Religion may keep this final straw of rationality: we don't and can't know everything given a (probably) infinite universe. Religion is not best understood as a theory of physics anyway, but rather as a study of history, society and mind.
[0] http://www.preposterousuniverse.com/blog/2009/06/17/timeless...
Is the idea that anything that science currently cannot explain must be connected to religion? That would be a fallacy.
As Alan Watts put it with his mischievous sense of humor:
"Science is the art of prediction"
Talking about religion, Christianity used to refer to this, then it lost its way. See eg.
This is still true, to an extent, in the Christian Orthodox world, Pseudo-Dionysius the Areopagite is still reguarded as one of the main “intellectual stars” (so to speak) of the Christian Orthodox thought. As for the “lost way” that you mention, I think that that change started in the West once the Reformartion took off and people wanted to “be sure” that they’ll get to live the eternal life. Here in Eastern Europe people do not think in absolute terms about life after death, as in nobody actually believes you can “earn” your way into Heaven, it all resides in God’s Will which is not possible for us to know. There’s also that New Testament parable of a guy asking Jesus at some point with whom of his wives will he be married in Heaven (the guy had been previously married to a different woman) and Jesus basically answered that that is a stupid question as nobody knows anything about Heaven.
> Jesus basically answered that that is a stupid question as nobody knows anything about Heaven.
Jesus said it was an ignorant question, yes, "You are in error because you do not know the Scriptures or the power of God." But he didn't say nobody knows. He said that she won't be married: "At the resurrection people will neither marry nor be given in marriage; they will be like the angels in heaven" (Matthew 22:29).
If the God, sitting on his throne in eternity, determines the fundamental to be eternity, then from that framed perspective, there is only eternity.
If the man, sitting on his porcelain throne in the bathroom, determines the fundamental to be a here-and-now framed by a past and future, then from that perspective, that is the truth.
It is all illusion, including eternity. There are only frames we may peer at infinity through.
We experience periodic phenomena, such as the cycles of days and years, the moon, our heartbeats, and our pace when walking. Even if some of these are not utterly uniform, the general observation that there are so many days in a year, etc., are objective in the sense that they are experienced by everybody. A concept of time could be formed by associating events with days, and noticing that some of the timelines formed in this way always point in the same direction. For instance, birth is to the left of death on this timeline, never the other way around. Now you've got a clock -- the sun -- and an arrow of time -- birth to death.
I describe a "theory of time" to myself in this way because I imagine that primitive people could form such a view, and find it useful enough to keep. For instance, knowing when it's time to plant, or when certain kinds of fish are likely to be found in a particular river, would improve the survival of a primitive group. At least, it would improve my survival in such a situation.
So I think, even if time and space break down on cosmic or microscopic scales, they are satisfactorily real.
http://www.preposterousuniverse.com/blog/2009/06/17/timeless...
Put it this way: clearly time appears to exist, at first glance. Even the timelessness crowd somehow manages to submit their essay competition entries by the deadline, and finish their Bloggingheads dialogues within an hour.
To paraphrase (but use the same example because it is funny): time doesn't appear at the fundamental concepts in physics. Cats also don't appear at the fundamental level of physics. But cats exist. Time (and our perception of it) must appear somewhere as a emergent feature.
Why are people so hung up on the question whether 'x' exist or not without actually having a proper idea of what it mean for something to "exist"?
In relativity it is particularly important. Timelike dimensions are treated differently in the metric, with a +1 or -1 depending on taste, ie
ds^2 = c dt^2 - dx_1^2 - dx_2^2 - dx_3^2,
so I don't think its quite fair to say that it doesn't "appear". In quantum physics unitary evolution is invertible. Decoherence is not reversible (I mean interaction - loss of entanglement).
Maybe these theories have been biased by our perception, but they are good (but incomplete) models.
1) There is no such thing as simultaneous. There is no universal now. 2) Time does not proceed at a constant rate 3) Time proceeds at different speeds for different observers.
So time as relativity defines it is certainly true. But time as people conceive it is fundamentally different. At best, common sense time is a profoundly special case that can't imagine the general case. And at worst, a nonsensical concept evolution gave us. Perhaps so erroneous it might be valid to say it does not exist.
It's the same how Newtonian Mechanics is a really good approximation (and still widely used, too), and because everything around us happens to obey it very closely, it is more intuitive. The difference between what Newton's equations and Einstein's equations predict for most planetary orbits is very slight.
We've already reached the point at which reductionism breaks down in physics: you can smoothly transform between electrons and magnetic monopoles by varying the fine structure parameter, so which one is made of which? The answer is "Whichever is more convenient at the moment." [0]
There are already nascent theories attempting to simplify quantum field theory, that could be considered fundamental, which are based entirely on geometric and combinatoric concepts where time isn't implicit in the definition of the theory (because it's just manipulations of polytopes) but where time emerges as a feature instead of being an assumption. [1][2]
[0]: https://www.youtube.com/watch?v=NZ-ElsvYKyo&index=2&list=PL3...
Sure, in that it is a component of a spacetime, and events happen at different points in spacetime.
How you slice up spacetime into space and time is essentially up to you. That is what Rovelli is talking about: it's not that there is no time, but rather that slicing up a spacetime in any fashion will still not produce a global "now".
Setting down a system of constant pseudo-Cartesian coordinates:
> ds^2 = c dt^2 - dx_1^2 - dx_2^2 - dx_3^2
(nit: c^2)
versus some other set of coordinates on the shame spacetime doesn't change a pair of infinitesimally close field-values on field filling that spacetime, nor their relative positions -- it just changes how one describes the latter.
We can still chose a now and describe the difference between now-1, now, now+1 as operations within the "now" spacelike hypersurface. However, does this justify a view that now+1 is undetermined at now-1? What operations happen where in the same volume of spacetime for an observer using a different slicing?
The exact metric is less interesting here than that the spacetime is Lorentzian; that feature is what constrains slicing choices within a causal cone, or alternatively provides the diffeomorphism invariance under arbitrary time parametrisation.
"Timelessness" doesn't get rid of that sort of ordering: a relativistic field's field-values at different points in spacetime depend on it, however one wants to formalize that dependency, e.g. they must transform under representations of the Poincaré group, Poincaré invariance must be implemented unitarily on the state space, or the action must be Poincaré-invariant.
What timelessness does challenge is some notions about operations within any spacelike hypersurface.
I thought that was just already accepted as part of relativity that there is no global now (I feel like you are saying there is no global interial reference frame?).
I really mean that there is this more general concept of time which looks like what humans perceive as "time" locally. The ordinary human perception of time is obviously not quite the whole picture. Our lives are just slow enough that we don't notice relativistic effects. We are just fooled into thinking its ordered linearly, but there is a more general picture.
But saying that there is no "time" because it doesn't quite match our intuitions is wrong. Its just that we have to expand our thinking.
Further, I think relativity still has an "arrow of time". Thermodynamic quantities can transform under reps of Poincare group - "Relativistic Thermodynamics" is certainly a thing. Landau and Lifshitz has a few chapters on it I believe. So the idea of time "passing" (entropy increasing at least carries over.
I'd be grateful if you could show me where in §27 (PDF pages 94-96) of http://people.physics.tamu.edu/kcolletti1/classes/fall15/sta... you get any of that from.
> "Relativistic Thermodynamics" is certainly a thing
Is it a thing which really deals with an arrow of time, or is it a thing which lets one study the temperature of a moving object, the temperature of an object in a gravitational field [Tolman], or the temperature of an object in which individual velocities (of fluid elements or particles) are large [Israel & Stewart]?
However it doesn't actually look like they reach a decisive conclusion - it is still for debate.
[0] http://iopscience.iop.org/article/10.1088/0305-4470/38/13/00... [1] https://arxiv.org/pdf/1802.07650.pdf
I think what you might be trying to argue is that in vacuum spacetime with a horizon there is a Gibbons-Hawking temperature T_{GH}. A Eulerian observer with a purely timelike worldline could measure T_{GH} at various points along its worldline. In de Sitter space the temperature is proportional to the Hubble parameter H.
Unfortunately, there is afaik no consistent or complete microphysical description of the Gibbons-Hawking effect. Additionally, it's so small that the presence of a relic matter field (like the cosmic microwave background) completely swamps it by many orders of magnitude (for H_0 it's 30 orders). So T_{GH}, purely general-relativistic, does not seem like a useful arrow of time in our universe until the latest of epochs maybe.
Look instead to the Boltzmann entropy of the matter; we can simply set a low-entropy boundary condition somewhere in spacetime, and then we do not even need to have an expanding universe to have higher entropy in spacetime at increasing distance from that boundary. Alternatively, we could go through some hoops to try to remove the boundary, as Hartle & Hawking among others.
Carroll has a list of relevant slides at https://www.slideshare.net/seanmcarroll/what-we-dont-know-ab...
None of this has much if any contact with relativistic thermodynamics. In cosmology we are almost always deliberately considering a family of privileged observers and ignoring the others (even though they exist). Our defined cosmological observers see matter (incl. radiation and any horizon radiation) as homogeneous and isotropic. Any expansion or contraction of space is an adiabatic process. \Lambda is nearly zero, but still sufficient to generate enormous spacetime curvature (the purely timelike worldlines of our observers are not parallel).
Finally, calculating in the cosmological frame is a convenience, nothing more.
I think this bit of truth was purposely hidden, as Einstein himself alluded to, by a dark cabal, and has coincidentally been rediscovered albeit as a secular institution primarily through a diefication of the scientific process.
Some of our still very early study of Quantum Mechanics points right to this matrix reality we experience.
However uncomfortable that may be.
Perhaps the emotion of time is precisely what time is for us.
The application of sufficient Time and Space can solve almost any problem. If 2 groups are in conflict, putting 10 light years and 100 million calendar years between them often removes the ability to conflict.
Hence to take a next big leap in understanding the cosmos we as a society will eventually need to be bold enough and open for other ideas regarding the truth of objective reality we experience in waking state. Could it be just like a dream, though a grand one, being projected by some cosmic consciousness of which we are inseparable part? Not some divine form I'm proposing here, but a formless pure consciousness awareness that each of us possess and experience it in silence. Eastern mystical traditions have long been investigating these alternative ideas and countless individuals have testified experiencing such super conscious state confirming the idea.
> To this blurring is added quantum indeterminacy. The ignorance that follows from this determines the existence of a particular variable—thermal time—and of an entropy that quantifies our uncertainty.
... and ...
> The variable “time” is one of many variables that describe the world. It is one of the variables of the gravitational field: At our scale, we do not register quantum fluctuations, hence it is possible to think of spacetime as determined. Hence we can think of spacetime as being as rigid as a table. This table has dimensions: the one that we call space, and the one along which entropy grows, called time. In our everyday life we move at low speeds in relation to the speed of light and so we do not perceive the discrepancies between the different proper times of different clocks, and the differences in speed at which time passes at different distances from a mass are too small for us to distinguish.
But whatever, I am moved to read his book :)
You can get isolated pockets of low entropy that appear (e.g. the human brain), but I think I've heard it described that there has to be thermodynamic pathways leading to such states. We understand parts of these pathways, but there are important aspects still left to figure out.
And of course, as you mentioned, the system as a whole is still increasing in entropy the entire time.
Imagine a mountain where height inversely correlates with entropy. The summit represents the very low entropy state of the big bang, and the second law of thermodynamics is an enormous steam-roller that is currently in the process of flattening the entire mountain. Then, us humans are simply pebbles that have been shaken loose and are dancing in the foothills. In a few billion or trillion or quadrillion years, all the dancing pebbles will have been crushed into a fine dust and spread across a perfectly flat, unchanging plane.
But they will have danced beautifully in the many years before.
This always confuses me a bit, why do we consider the first instants of the universe maximally ordered? A near homogeneous sea of per-subatomic particles seems less ordered than the later universe of galaxies and stars and hydrogen atoms with cold areas in between.
One point that seems not to feature in these debates is that this is all (physics) fundamentally subject to the constraints of language (maths) and cognition (human), we choose to describe things in a way that appears useful to us, but these judgements and perceptions are filtered by how we understand things. We are squashy and small and it is quite silly to imagine we really are thinking about these processes in an objectively meaningful way.
Note what happens as the universe proceeds from that time period to its heat death; hydrogen is burned into higher elements until everything is cold iron floating in space. In this case, it might be best just to look at the available energy as a proxy for entropy; a universe full of hydrogen is a low-entropy universe that still has a lot of useful energy that can be extracted, whereas in the heat death of the universe, there's nothing left. No fusion can be done. No fission can be done. No chemical energy floating around that you can use. Just balls of iron in maximally thermalized environments, all maxed out in entropy.
As I've occasionally said in other contexts, right now the universe is young and awash in energy in many forms; our energy problem is a difficulty in figuring out the right way to metaphorically cup our hands and capture it all in the ways we want to use it. We're literally billions of years away from an actual lack of energy, because the universe started out with a lot of it.
Much higher ordering is straightforward and is essentially just statmech:
1. Run the expansion history of the universe backwards: there are fewer degrees of freedom as the universe collapses into the big bang.
2. Run the expansion history of the universe forwards: vacuum is very high entropy (you can swap a bit of vacuum from here with a bit of vacuum from there and not tell the difference), and there is much more of it at late epochs. Assuming no-hair, black holes are also very high entropy, and there are more of them at later epochs.
Maximal ordering makes some assumptions about quantum gravity with respect to (1):
> A near homogeneous sea of per-subatomic particles
... would expand in such a way that the universe would remain (nearly) perfectly smooth at all epochs.
We can start with the idea that there is an inherent uncertainty to the energy of empty-of-particles space. At later epochs, this uncertainty is small; but in the very early universe it is large. With slow expansion, the uncertainties average out over short distances. However, during cosmic inflation, the uncertainties are stretched and only average out on much larger length scales. The "new" vacuum produced as inflation continues has prorgressively less energy uncertainty, but are "within" the streched uncertainties from earlier. By the time inflation ends, random regions of all sizes contain subregions of overdense and underdense vacuum energy.
Cosmic inflation precedes the hot big bang: it is the chaotic arrangement of vacuum energy at different densities that decays into matter (in the most general sense of matter) proportional to the vacuum energy density. More matter arises in the overdense regions than in the underdense regions. As expansion progresses, gravitation takes over: light finds it easier to leave underdense regions than overdense regions, and that (the gravitational redshift, and the spectrum being highly similar to blackbody radiation) means underdense regions look slightly hotter than average regions, and overdense regions look slightly colder. Gravitation also works on the rest of matter too, not just light: matter flows from underdense regions to denser regions; matter flows to overdense regions from sparser regions. Finally, overly-overdense regions will heat up and emit light and kick hot particles out. The balances between the vacuum energy fluctuations before the hot big bang and the gravitation-vs-radiation flow of matter afterwards are encoded in the cosmic microwave background.
> less ordered than the universe of galaxies and stars and hydrogen atoms with cold areas in between
The mostly-empty areas in between have much higher entropy, and those areas are even bigger (and emptier) at later times. The galaxies and stars and hydrogen atoms are not more numerous at later times: matter dilutes away with expansion.
Imagine the soil 50 years before Shakespeare forming the food he ate and the trees which became the paper he wrote on. It seems a lot like ash (soil) did organize itself to a lower entropy collection (with a lot of help from an external energy pool).
Also, many seeds didn't make it, so there is a bit of survivor bias looking at the one seed that did become a tree.
Chapter 2
The Formulation of Quantum Mechanics
2.1
Basic Theoretical Concepts
Every physical theory involves some basic physical concepts, a mathemati- cal formalism, and set of correspondence rules which map the physical concepts onto the mathematical objects that represent them. The correspondence rules are first used to express a physical problem in mathematical terms. Once the mathematical version of the problem is formulated, it may be solved by purely mathematical techniques that need not have any physical interpretation. The formal solution is then translated back into the physical world by means of the correspondence rules.
Sometimes this mapping between physical and mathematical objects is so obvious that we need not think about it. In classical mechanics the position of a particle (physical concept) is mapped onto a real number or a set of real numbers (mathematical concept). Although the notion of a real number in pure mathematics is not trivial, this correspondence rule can be grasped intuitively by most people, without any risk of confusion. The mathematical formalism of quantum mechanics is much more abstract and less intuitive than that of classical mechanics. The world does not appear to be made up of Hermi- tian operators and infinite-dimensional state vectors, and we must give careful and explicit attention to the correspondence rules that relate the abstract mathematical formalism to observable reality.
Of course, binary as a notion is simply a set of relative measurements of the peaks and troughs of a wave at a specific time and scale, therefore we may deduce the ultimate excitation of all, what appears as this large number, is an analog, encompasses everything, and our reality a carefully crafted series of reductions from this source.
Wonderful and awe inspiringly scary that we may even consider such a thing of brilliance.
Perhaps the difference between an approximation and a complete encoding should be emphasised more forcefully on CS courses.
On the other hand, if there are non computable processes at work in reality, then not everything.
Who else dislikes this sort of pop-science writing? It seems to care more about evoking some mystical and philosophical idea of the universe than effectively communicating the science.
@Westoncb: Philosophy of science is about as useful to scientists as ornithology is to birds.
What is wrong about mystical, philosophical idea of the universe? I like mystical, philosophical idea of the universe.
--R. Feynman
A: I like x
B: I don't like x
A: Why?
B: Because it is not science
A: Why is that bad?
B: It is not. Because R.Feynman said blah blah blah...
A: ??
How can it soften the principles of science, if it does not masquerade as science. Can you point me in the article where it tries to pass some mysticism or philosophy as science?
> Reality: The details of time diverge a bit from common understanding.
I think you may be underestimating the divergence a bit. The author is hardly alone in finding general relativity's implications on time to be of profound philosophical importance, for instance.
http://blog.rongarret.info/2014/10/parallel-universes-and-ar...
I love pop science writing. The thing is that this easy imagination helps a lot of people access hitherto unknowable principles of science. If you are science oriented or enquiry minded but do not have a background in the extreme detail required to access the specific subject/topic, you would have very likely never learnt anything about it given the arcane approach road to it. Popular science writing makes those spaces accessible, marks the roads, explains the possibilities and allows one to think through those abstractions. Then if you are sufficiently interested, you actually get into the hairy details of the actual science. But for most of us who are actually just traveling and understanding, this sort of writing gives us a grip of the "lay of the land."
I look at such writing as maps of knowledge, not the actual thing, but sufficiently detailed and made interesting to give people a sense of where they are. It's a jungle gym for the thinking mind.
Such bullshit. QM does not govern events. The probability function encodes everything about how it's governed. QM does not speak to that at all. Unitarity assumes the probability function remains correct. That doesn't mean the probability function does not have any inputs which can be influenced by change. Dumb article